"The government, the Social Democrats, the Danish People's Party, the Liberal Alliance and the Conservative People's Party have agreed to amend the bill concerning valuables," a government statement said, indicating that wedding rings and other items of sentimental value would be exempt from the move.
In addition to wedding rings, it listed engagement rings, family portraits and badges of honour as items that could not be confiscated from asylum seekers.
Items such as watches, mobile phones and computers may still be seized, it said.
The proposal is part of a bigger immigration bill the Danish parliament is due to begin debating on Wednesday.
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A vote will be held on January 26 but two right-wing parties that back the minority government in parliament, as well as the opposition Social Democrats, had demanded changes be made to the rules outlining what could be confiscated from migrants.
Integration Minister Inger Stojberg has faced a storm of criticism over the plans to search migrants' bags for gold and other valuables, prompting some commentators to draw parallels to Nazi Germany.
The bill will also delay family reunifications for some refugees by up to three years.